TITLE by Wei Tang
# Load the Data
wine <- read.csv("wineQualityReds.csv")
wine$X <- NULL## 'data.frame': 1599 obs. of 12 variables:
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...## fixed.acidity volatile.acidity citric.acid residual.sugar
## Min. : 4.60 Min. :0.1200 Min. :0.000 Min. : 0.900
## 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090 1st Qu.: 1.900
## Median : 7.90 Median :0.5200 Median :0.260 Median : 2.200
## Mean : 8.32 Mean :0.5278 Mean :0.271 Mean : 2.539
## 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420 3rd Qu.: 2.600
## Max. :15.90 Max. :1.5800 Max. :1.000 Max. :15.500
## chlorides free.sulfur.dioxide total.sulfur.dioxide
## Min. :0.01200 Min. : 1.00 Min. : 6.00
## 1st Qu.:0.07000 1st Qu.: 7.00 1st Qu.: 22.00
## Median :0.07900 Median :14.00 Median : 38.00
## Mean :0.08747 Mean :15.87 Mean : 46.47
## 3rd Qu.:0.09000 3rd Qu.:21.00 3rd Qu.: 62.00
## Max. :0.61100 Max. :72.00 Max. :289.00
## density pH sulphates alcohol
## Min. :0.9901 Min. :2.740 Min. :0.3300 Min. : 8.40
## 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500 1st Qu.: 9.50
## Median :0.9968 Median :3.310 Median :0.6200 Median :10.20
## Mean :0.9967 Mean :3.311 Mean :0.6581 Mean :10.42
## 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300 3rd Qu.:11.10
## Max. :1.0037 Max. :4.010 Max. :2.0000 Max. :14.90
## quality
## Min. :3.000
## 1st Qu.:5.000
## Median :6.000
## Mean :5.636
## 3rd Qu.:6.000
## Max. :8.000## 'data.frame': 1599 obs. of 13 variables:
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...
## $ quality.level : Ord.factor w/ 3 levels "high"<"average"<..: 2 2 2 2 2 2 2 1 1 2 ...Our dataset consists of 12 variables, with 1599 observations. Quality variable is discrete and the others are continuous.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 3.000 5.000 6.000 5.636 6.000 8.000Red wine quality is normally distributed and concentrated around 5 and 6.
Red wine quality is normally distributed and concentrated on average.
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## [1] 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 6.7 7.5 5.6
## [14] 7.8 8.9 8.9 8.5 8.1 7.4 7.9 8.9 7.6 7.9 8.5 6.9 6.3
## [27] 7.6 7.9 7.1 7.8 6.7 6.9 8.3 6.9 5.2 7.8 7.8 8.1 5.7
## [40] 7.3 7.3 8.8 7.5 8.1 6.8 4.6 7.7 8.7 6.4 5.6 8.8 6.6
## [53] 6.6 8.6 7.6 7.7 10.2 7.5 7.8 7.3 8.8 7.7 7.5 7.0 7.2
## [66] 7.2 7.5 6.6 9.3 8.0 7.7 7.7 7.7 8.3 9.7 8.8 8.8 6.8
## [79] 6.7 8.3 6.2 7.8 7.4 7.3 6.3 6.9 8.6 7.7 9.3 7.0 7.9
## [92] 8.6 8.6 7.7 5.0 4.7 6.8 7.0 7.6 8.1 8.3 7.8 8.1 8.1
## [105] 7.2 8.1 7.8 6.2 8.0 8.1 7.8 8.4 8.4 10.1 7.8 9.4 8.3
## [118] 7.8 8.8 7.0 7.3 8.8 7.3 8.0 7.8 9.0 8.2 8.1 8.0 6.1
## [131] 8.0 5.6 5.6 6.6 7.9 8.4 8.3 7.2 7.8 7.8 8.4 8.3 5.2
## [144] 6.3 5.2 8.1 5.8 7.6 6.9 8.2 7.3 9.2 7.5 7.5 7.1 7.1
## [157] 7.1 7.1 7.1 6.8 7.6 7.6 7.8 7.4 7.3 7.8 6.8 7.3 6.8
## [170] 7.5 7.9 8.0 8.0 7.4 7.3 6.9 7.3 7.5 7.0 8.8 8.8 8.9
## [183] 7.2 6.8 6.7 8.9 7.4 7.7 7.9 7.9 8.2 6.4 6.8 7.6 7.6
## [196] 7.8 7.3 11.5 5.4 6.9 9.6 8.8 6.8 7.0 7.0 12.8 12.8 7.8
## [209] 7.8 11.0 9.7 8.0 11.6 8.2 7.8 7.0 8.7 8.1 7.5 7.8 7.8
## [222] 7.4 6.8 8.6 8.4 7.7 8.9 9.0 7.7 6.9 5.2 8.0 8.5 6.9
## [235] 8.2 7.2 7.2 7.2 7.2 8.2 8.9 12.0 7.7 15.0 15.0 7.3 7.1
## [248] 8.2 7.7 7.3 10.8 7.1 11.1 7.7 7.1 8.0 9.4 6.6 7.7 10.0
## [261] 7.9 7.0 8.0 7.9 12.5 11.8 8.1 7.9 6.9 11.5 7.9 11.5 10.9
## [274] 8.4 7.5 7.9 6.9 11.5 10.3 8.9 11.4 7.7 7.6 8.9 9.9 9.9
## [287] 12.0 7.5 8.7 11.6 8.7 11.0 10.4 6.9 13.3 10.8 10.6 7.1 7.2
## [300] 6.9 7.5 11.1 8.3 7.4 8.4 10.3 7.6 10.3 10.3 7.4 10.3 7.9
## [313] 9.0 8.6 7.4 7.1 9.6 9.6 9.8 9.6 9.8 9.3 7.8 10.3 10.0
## [326] 10.0 11.6 10.3 13.4 10.7 10.2 10.2 8.0 8.4 7.9 11.9 8.9 7.8
## [339] 12.4 12.5 12.2 10.6 10.9 10.9 11.9 7.0 6.6 13.8 9.6 9.1 10.7
## [352] 9.1 7.7 13.5 6.1 6.7 11.5 10.5 11.9 12.6 8.2 8.6 11.9 12.5
## [365] 12.8 10.0 12.8 10.4 10.3 9.4 6.9 7.9 9.1 7.4 14.0 11.5 11.5
## [378] 9.4 11.4 8.3 8.3 13.7 8.3 8.3 7.7 7.4 7.8 8.3 7.8 9.6
## [391] 5.6 13.7 9.5 8.4 12.7 12.0 6.6 11.5 11.5 8.7 6.6 7.7 12.2
## [404] 11.4 7.7 8.7 9.8 12.0 10.4 12.5 9.0 9.1 7.1 9.9 8.8 8.6
## [417] 10.6 7.0 11.9 6.8 9.5 6.6 7.7 10.5 7.7 6.6 6.4 9.5 9.1
## [430] 12.8 10.5 7.8 11.9 12.3 10.4 12.3 8.0 11.1 10.4 7.0 12.6 11.9
## [443] 15.6 10.0 5.3 9.5 12.5 9.3 8.6 11.9 11.9 8.4 6.8 10.4 7.0
## [456] 11.3 8.9 9.2 10.4 11.6 9.2 8.3 11.0 8.1 11.5 10.0 10.3 8.8
## [469] 11.4 8.7 13.0 9.6 12.5 9.9 10.5 9.6 9.3 10.4 9.6 9.4 10.6
## [482] 9.4 10.6 10.6 10.6 10.2 10.2 10.2 11.6 9.3 9.3 9.2 8.9 8.7
## [495] 6.5 10.7 7.8 7.2 10.7 8.7 7.8 10.4 10.4 10.5 10.5 10.2 10.4
## [508] 11.2 10.0 13.3 12.4 10.0 10.7 10.5 10.5 8.5 12.5 10.4 10.9 7.3
## [521] 9.8 7.6 8.2 9.3 9.2 10.4 7.3 7.0 8.2 9.9 9.1 11.9 11.9
## [534] 10.3 10.0 9.1 9.9 8.1 12.9 11.2 9.2 9.5 9.3 11.2 14.3 9.1
## [547] 7.5 10.6 12.4 9.0 6.8 9.4 9.5 5.0 15.5 15.5 10.9 15.6 10.9
## [560] 13.0 12.7 9.0 9.0 7.6 13.0 12.7 8.7 8.7 9.8 6.2 11.5 6.2
## [573] 10.2 10.5 10.6 12.3 9.9 8.8 8.8 10.6 12.3 12.3 11.7 12.0 11.8
## [586] 7.6 11.1 7.3 5.0 10.2 9.0 6.6 9.0 9.9 7.9 8.9 12.4 11.9
## [599] 8.5 12.7 8.2 13.2 7.7 13.2 8.3 8.3 9.4 8.8 10.1 6.3 8.8
## [612] 13.2 7.5 8.2 9.2 9.6 9.6 11.5 11.4 11.3 8.3 8.2 10.0 7.9
## [625] 6.8 6.8 8.8 8.8 8.7 7.6 8.7 10.4 7.6 10.1 7.9 8.7 9.6
## [638] 9.5 7.7 8.9 9.9 9.5 9.9 9.5 9.9 7.8 7.3 8.3 8.7 6.7
## [651] 10.7 9.8 15.9 9.4 8.6 9.7 10.7 12.0 7.2 7.1 7.2 7.5 7.2
## [664] 10.1 12.1 9.4 8.3 11.3 10.0 11.3 6.9 8.2 9.8 8.2 10.8 9.3
## [677] 10.8 8.6 8.3 10.8 13.3 8.0 8.5 8.1 9.8 8.1 7.1 9.1 7.7
## [690] 8.1 7.4 9.2 8.6 9.0 9.0 5.1 7.0 7.0 9.4 11.8 10.6 7.0
## [703] 7.0 7.5 9.1 8.4 7.0 7.4 7.8 9.7 10.6 8.9 8.7 8.0 9.9
## [716] 7.2 8.0 7.6 8.4 7.1 8.4 8.9 7.6 7.1 7.5 9.0 8.1 6.4
## [729] 6.4 6.4 9.5 8.9 7.3 7.0 7.7 7.7 7.7 8.2 9.0 9.0 8.3
## [742] 9.2 6.5 11.6 11.1 7.3 8.2 8.6 7.2 7.3 8.3 8.3 7.6 8.3
## [755] 7.8 7.8 6.3 8.1 8.1 8.8 9.0 9.3 8.8 9.3 9.1 9.2 8.8
## [768] 7.5 7.1 7.9 7.1 9.4 9.5 7.9 7.9 7.2 6.9 6.9 8.3 7.1
## [781] 7.0 6.5 9.0 6.5 7.1 9.9 9.9 10.0 10.0 8.6 7.4 8.8 7.1
## [794] 7.7 10.1 10.8 8.7 9.3 9.4 9.4 7.2 8.6 5.1 7.7 8.4 8.2
## [807] 8.4 8.2 7.4 7.6 7.3 12.9 10.8 6.9 12.6 10.8 9.8 10.8 7.1
## [820] 9.1 7.0 4.9 6.7 6.7 7.1 7.1 7.5 7.1 7.8 5.9 7.5 5.9
## [833] 10.4 11.6 8.8 7.6 6.7 6.7 10.1 6.0 11.1 6.6 10.6 7.1 9.9
## [846] 6.4 6.4 7.4 6.4 6.4 9.3 9.3 8.0 9.3 9.3 7.6 9.3 8.2
## [859] 11.7 6.8 7.2 5.8 7.5 7.2 7.2 7.2 6.8 6.9 6.8 7.6 7.7
## [872] 6.9 7.3 9.1 10.4 8.8 7.1 7.7 8.8 7.2 9.2 7.6 8.4 7.2
## [885] 8.8 8.9 9.0 10.7 6.8 10.7 7.2 7.2 10.1 7.2 7.2 7.1 8.3
## [898] 7.1 8.3 8.3 8.9 7.4 7.4 6.8 6.8 9.2 7.2 6.1 7.4 7.3
## [911] 9.3 9.1 10.0 9.4 7.3 8.6 5.3 6.8 8.4 8.4 9.6 8.4 8.4
## [924] 6.8 8.6 8.6 9.4 8.4 8.6 8.7 6.6 7.4 7.6 7.4 6.6 8.8
## [937] 8.8 12.0 7.2 6.2 9.6 9.9 10.1 9.8 8.3 10.2 10.2 8.3 8.9
## [950] 8.9 8.9 8.3 8.2 10.2 7.6 8.5 9.0 9.5 6.4 8.0 8.5 7.1
## [963] 6.6 8.8 8.5 8.3 9.0 8.5 9.0 6.7 10.4 10.4 10.1 8.5 8.8
## [976] 7.2 7.2 8.4 7.0 12.2 9.1 9.5 7.3 9.1 12.2 7.4 9.8 7.1
## [989] 7.7 9.7 7.7 7.1 6.5 7.1 10.0 7.7 5.6 5.6 8.9 6.4 7.5
## [1002] 9.9 9.1 6.8 8.2 6.8 9.1 9.1 8.9 9.6 8.9 8.9 7.7 7.5
## [1015] 8.0 10.5 8.9 8.0 8.0 7.0 11.3 11.3 7.0 8.2 7.7 8.6 7.9
## [1028] 6.4 7.2 7.7 7.1 7.3 8.1 7.5 8.9 10.1 7.6 7.3 8.7 8.9
## [1041] 7.4 6.9 8.9 9.5 6.4 6.9 7.6 7.1 9.3 9.3 7.1 8.5 5.6
## [1054] 8.3 8.2 8.2 8.9 7.6 9.9 8.9 11.6 9.1 8.0 10.2 8.2 7.7
## [1067] 6.6 11.1 11.1 8.0 9.3 7.5 7.2 8.0 7.5 9.1 9.9 8.6 8.6
## [1080] 7.9 10.3 7.9 7.2 8.7 7.2 6.8 8.5 7.9 11.6 11.6 10.0 7.9
## [1093] 7.0 9.2 6.6 9.4 6.6 8.6 8.0 8.6 8.4 7.4 6.1 7.4 8.0
## [1106] 6.3 8.2 9.1 8.1 10.8 8.3 5.4 7.9 8.9 5.0 7.0 7.0 7.0
## [1119] 7.1 5.6 7.9 6.6 6.3 10.7 6.5 8.8 5.8 6.3 10.0 10.5 9.1
## [1132] 5.9 7.4 7.2 8.5 8.0 10.4 10.4 7.5 8.2 7.3 8.2 6.9 7.0
## [1145] 7.3 8.2 7.8 10.0 7.8 10.0 8.2 6.1 8.3 9.6 6.6 8.3 8.5
## [1158] 5.1 6.7 10.2 10.6 8.8 8.5 9.0 9.0 8.5 9.9 8.2 6.5 7.6
## [1171] 9.2 7.1 9.7 7.6 7.6 6.5 6.5 7.1 5.6 8.2 8.2 9.8 10.2
## [1184] 6.8 6.7 7.0 6.6 7.0 6.7 8.8 9.1 6.5 7.2 6.4 7.0 6.2
## [1197] 7.9 7.7 7.7 7.9 7.7 7.9 8.6 9.9 7.2 7.2 7.2 9.9 7.2
## [1210] 6.2 6.8 6.6 6.8 9.6 10.2 8.8 7.9 8.2 8.2 9.0 10.9 10.9
## [1223] 8.1 10.5 12.6 9.2 7.5 9.0 5.1 7.6 7.7 7.8 7.6 10.2 7.1
## [1236] 6.0 7.8 7.1 8.1 6.5 7.5 9.8 9.0 8.3 5.9 7.4 7.4 7.4
## [1249] 6.9 7.1 7.1 7.5 7.1 7.9 7.8 6.1 7.5 7.0 6.8 6.8 8.6
## [1262] 6.3 9.8 8.2 8.5 7.2 7.2 10.4 6.9 5.5 5.0 7.3 5.9 7.5
## [1275] 7.8 8.0 8.5 7.0 8.0 9.8 7.1 7.1 7.9 8.7 7.0 11.3 7.1
## [1288] 8.0 7.0 7.0 7.6 8.2 5.9 7.5 8.2 6.6 6.6 7.2 5.7 7.6
## [1301] 5.2 6.7 9.1 8.0 7.6 7.5 9.7 6.8 9.7 7.0 7.5 6.5 8.0
## [1314] 7.0 7.0 7.5 5.4 9.9 7.5 9.1 9.7 5.0 9.1 9.1 6.7 6.7
## [1327] 6.7 6.7 6.5 7.4 7.4 7.8 8.4 9.1 7.2 6.6 6.0 6.0 6.0
## [1340] 7.5 7.5 7.5 7.6 7.5 11.5 8.2 6.1 7.2 7.2 6.9 9.0 7.2
## [1353] 7.6 7.6 7.2 6.1 6.1 7.3 7.4 11.6 9.2 8.3 11.6 8.0 7.2
## [1366] 7.8 7.3 6.9 8.0 6.6 8.7 7.5 8.7 7.7 6.8 7.2 8.2 5.2
## [1379] 7.2 7.5 7.5 6.8 8.0 8.0 7.1 8.0 7.4 7.4 6.6 6.7 6.0
## [1392] 8.0 7.1 8.0 6.4 8.6 8.7 7.3 7.0 7.2 7.9 7.9 7.6 7.2
## [1405] 8.0 7.7 8.2 6.0 8.1 6.0 6.6 6.4 8.2 9.9 10.0 6.2 10.0
## [1418] 7.3 7.8 7.7 7.8 7.5 7.0 6.4 8.3 8.3 7.7 7.6 7.8 7.9
## [1431] 7.4 7.6 5.9 6.1 10.2 10.2 10.0 6.8 7.0 7.3 7.2 7.4 6.9
## [1444] 6.9 7.3 7.4 6.9 6.8 6.9 7.2 7.2 7.8 6.6 7.6 11.7 6.5
## [1457] 6.0 7.6 8.4 7.9 6.4 6.2 6.8 6.9 6.8 6.8 7.3 6.7 7.3
## [1470] 7.3 10.0 6.7 7.6 6.1 9.9 5.3 9.9 5.3 7.1 8.2 5.6 8.2
## [1483] 7.2 8.1 6.8 7.0 6.8 6.0 5.6 6.2 7.1 5.6 6.2 7.7 6.4
## [1496] 7.0 7.7 6.9 6.6 6.9 7.5 7.8 7.3 6.2 7.5 6.7 6.8 7.5
## [1509] 7.1 7.9 6.4 7.1 6.4 6.4 6.9 6.9 6.1 6.5 7.4 6.6 6.5
## [1522] 6.9 6.1 6.8 6.0 6.7 6.8 7.1 7.9 7.1 6.6 6.1 7.2 8.0
## [1535] 6.6 7.0 6.1 5.4 6.2 7.2 6.2 7.4 6.7 11.1 8.4 6.5 7.0
## [1548] 6.3 11.2 7.4 7.1 7.1 6.3 7.3 6.6 7.0 6.6 6.6 6.9 7.8
## [1561] 7.8 7.8 7.2 7.2 7.2 6.7 6.7 7.2 7.0 6.2 6.4 6.4 7.3
## [1574] 6.0 5.6 7.5 8.0 6.2 6.8 6.2 7.4 6.2 6.1 6.2 6.7 7.2
## [1587] 7.5 5.8 7.2 6.6 6.3 5.4 6.3 6.8 6.2 5.9 6.3 5.9 6.0
The distribution of fixed acidity is right skewed, and concentrated around 8
cutting the outliers
## [1] 0.700 0.880 0.760 0.280 0.700 0.660 0.600 0.650 0.580 0.500 0.580
## [12] 0.500 0.615 0.610 0.620 0.620 0.280 0.560 0.590 0.320 0.220 0.390
## [23] 0.430 0.490 0.400 0.390 0.410 0.430 0.710 0.645 0.675 0.685 0.655
## [34] 0.605 0.320 0.645 0.600 0.380 1.130 0.450 0.450 0.610 0.490 0.660
## [45] 0.670 0.520 0.935 0.290 0.400 0.310 0.660 0.520 0.500 0.380 0.510
## [56] 0.620 0.420 0.630 0.590 0.390 0.400 0.690 0.520 0.735 0.725 0.725
## [67] 0.520 0.705 0.320 0.705 0.630 0.670 0.690 0.675 0.320 0.410 0.410
## [78] 0.785 0.750 0.625 0.450 0.430 0.500 0.670 0.300 0.550 0.490 0.490
## [89] 0.390 0.620 0.520 0.490 0.490 0.490 1.020 0.600 0.775 0.500 0.900
## [100] 0.545 0.610 0.500 0.545 0.575 0.490 0.575 0.410 0.630 0.330 0.785
## [111] 0.560 0.620 0.600 0.310 0.560 0.400 0.540 0.560 0.550 0.690 1.070
## [122] 0.550 0.695 0.710 0.500 0.620 1.330 1.330 0.590 0.380 0.745 0.500
## [133] 0.500 0.500 1.040 0.745 0.715 0.415 0.560 0.560 0.745 0.715 0.340
## [144] 0.390 0.340 0.670 0.680 0.490 0.490 0.400 0.330 0.520 0.600 0.600
## [155] 0.430 0.430 0.430 0.430 0.680 0.600 0.950 0.680 0.530 0.600 0.590
## [166] 0.630 0.640 0.550 0.630 0.705 0.885 0.420 0.420 0.620 0.380 0.500
## [177] 0.380 0.520 0.805 0.610 0.610 0.610 0.730 0.610 0.620 0.310 0.390
## [188] 0.705 0.500 0.490 0.500 0.370 0.630 0.550 0.550 0.590 0.580 0.300
## [199] 0.835 1.090 0.320 0.370 0.500 0.420 0.430 0.300 0.300 0.570 0.440
## [210] 0.300 0.530 0.725 0.440 0.570 0.735 0.490 0.625 0.725 0.490 0.530
## [221] 0.340 0.530 0.610 0.645 0.635 0.430 0.590 0.820 0.430 0.520 0.480
## [232] 0.380 0.370 0.520 1.000 0.630 0.630 0.645 0.630 1.000 0.635 0.380
## [243] 0.580 0.210 0.210 0.660 0.680 0.600 0.530 0.660 0.320 0.600 0.350
## [254] 0.775 0.600 0.570 0.340 0.695 0.410 0.310 0.330 0.975 0.520 0.370
## [265] 0.560 0.260 0.870 0.350 0.540 0.180 0.545 0.180 0.370 0.715 0.650
## [276] 0.545 0.540 0.180 0.320 0.400 0.260 0.270 0.520 0.400 0.590 0.590
## [287] 0.450 0.400 0.520 0.420 0.520 0.200 0.550 0.360 0.340 0.500 0.830
## [298] 0.630 0.650 0.670 0.530 0.180 0.705 0.670 0.650 0.530 0.620 0.410
## [309] 0.430 0.290 0.530 0.530 0.460 0.470 0.360 0.350 0.560 0.770 0.660
## [320] 0.770 0.660 0.610 0.620 0.590 0.490 0.490 0.530 0.440 0.270 0.460
## [331] 0.360 0.360 0.580 0.560 0.650 0.695 0.430 0.430 0.490 0.280 0.340
## [342] 0.420 0.390 0.390 0.570 0.685 0.815 0.490 0.560 0.785 0.670 0.795
## [353] 0.665 0.530 0.210 0.750 0.410 0.420 0.430 0.380 0.700 0.450 0.580
## [364] 0.460 0.615 0.420 0.615 0.575 0.340 0.270 0.765 0.240 0.280 0.550
## [375] 0.410 0.540 0.450 0.270 0.625 0.420 0.260 0.415 0.260 0.260 0.510
## [386] 0.630 0.540 0.660 0.460 0.380 0.850 0.415 0.370 0.665 0.600 0.370
## [397] 0.735 0.590 0.590 0.765 0.735 0.260 0.480 0.600 0.690 0.310 0.440
## [408] 0.390 0.340 0.460 0.430 0.450 0.735 0.400 0.520 0.725 0.480 0.580
## [419] 0.380 0.770 0.560 0.840 0.960 0.240 0.960 0.840 0.670 0.780 0.520
## [430] 0.840 0.240 0.550 0.370 0.390 0.410 0.390 0.670 0.450 0.410 0.620
## [441] 0.310 0.400 0.685 0.440 0.570 0.735 0.380 0.480 0.530 0.390 0.390
## [452] 0.370 0.560 0.330 0.230 0.620 0.590 0.630 0.330 0.580 0.430 0.615
## [463] 0.260 0.660 0.315 0.290 0.500 0.460 0.360 0.820 0.320 0.540 0.370
## [474] 0.350 0.280 0.680 0.270 0.240 0.680 0.685 0.280 0.300 0.360 0.360
## [485] 0.440 0.670 0.670 0.645 0.320 0.390 0.775 0.410 0.400 0.690 0.390
## [496] 0.350 0.520 0.340 0.350 0.690 0.520 0.440 0.440 0.260 0.240 0.490
## [507] 0.240 0.670 0.590 0.290 0.420 0.590 0.400 0.510 0.510 0.655 0.600
## [518] 0.610 0.210 0.365 0.250 0.410 0.390 0.400 0.430 0.640 0.365 0.380
## [529] 0.420 0.630 0.220 0.380 0.380 0.270 0.480 0.220 0.630 0.825 0.350
## [540] 0.500 0.590 0.460 0.715 0.660 0.310 0.470 0.550 0.310 0.350 0.530
## [551] 0.510 0.430 0.460 1.040 0.645 0.645 0.530 0.645 0.530 0.470 0.600
## [562] 0.440 0.540 0.290 0.470 0.600 0.700 0.700 0.500 0.360 0.350 0.360
## [573] 0.240 0.590 0.340 0.270 0.500 0.440 0.470 0.310 0.500 0.500 0.490
## [584] 0.280 0.330 0.510 0.310 0.730 0.420 0.290 0.450 0.390 0.450 0.490
## [595] 0.720 0.595 0.400 0.580 0.585 0.590 0.915 0.460 0.835 0.460 0.580
## [606] 0.600 0.410 0.480 0.650 0.360 0.240 0.380 0.640 0.390 0.755 0.600
## [617] 0.600 0.310 0.460 0.370 0.540 0.560 0.580 0.510 0.690 0.690 0.600
## [628] 0.600 0.540 0.685 0.540 0.280 0.410 0.935 0.350 0.840 0.880 0.885
## [639] 0.915 0.290 0.540 0.590 0.540 0.590 0.540 0.640 0.670 0.845 0.480
## [650] 0.420 0.430 0.880 0.360 0.330 0.470 0.550 0.430 0.500 0.520 0.840
## [661] 0.520 0.420 0.570 0.280 0.400 0.590 0.490 0.340 0.730 0.340 0.400
## [672] 0.730 1.240 0.730 0.400 0.410 0.400 0.800 0.780 0.260 0.430 0.450
## [683] 0.460 0.780 0.980 0.780 0.650 0.640 0.660 0.380 1.185 0.920 0.490
## [694] 0.480 0.470 0.470 0.650 0.650 0.615 0.380 1.020 0.650 0.640 0.380
## [705] 0.765 1.035 0.780 0.490 0.545 0.310 1.025 0.565 0.690 0.430 0.740
## [716] 0.490 0.430 0.460 0.560 0.660 0.560 0.480 0.420 0.310 1.115 0.660
## [727] 0.720 0.570 0.570 0.865 0.550 0.875 0.835 0.450 0.560 0.965 0.965
## [738] 0.590 0.460 0.690 0.760 0.530 0.615 0.410 0.390 0.510 0.340 0.330
## [749] 0.500 0.510 0.650 0.650 0.540 0.650 0.480 0.910 0.980 0.870 0.870
## [760] 0.420 0.580 0.655 0.700 0.655 0.680 0.670 0.590 0.600 0.590 0.720
## [771] 0.590 0.685 0.570 0.400 0.400 1.000 0.765 0.635 0.430 0.520 0.570
## [782] 0.460 0.820 0.460 0.590 0.350 0.350 0.560 0.560 0.630 0.370 0.640
## [793] 0.610 0.600 0.270 0.890 0.460 0.370 0.500 0.500 0.610 0.550 0.585
## [804] 0.560 0.520 0.280 0.250 0.280 0.530 0.480 0.490 0.500 0.450 0.390
## [815] 0.410 0.450 0.510 0.290 0.715 0.660 0.685 0.420 0.540 0.540 0.480
## [826] 0.460 0.270 0.460 0.570 0.610 0.685 0.610 0.440 0.470 0.685 0.665
## [837] 0.280 0.280 0.310 0.500 0.420 0.660 0.500 0.685 0.250 0.640 0.640
## [848] 0.680 0.640 0.630 0.430 0.430 0.420 0.360 0.360 0.735 0.360 0.260
## [859] 0.280 0.560 0.620 1.010 0.420 0.620 0.620 0.635 0.490 0.510 0.560
## [870] 0.630 0.715 0.560 0.350 0.210 0.380 0.310 0.470 0.715 0.610 0.600
## [881] 0.560 0.715 0.310 0.600 0.610 0.750 0.800 0.520 0.570 0.900 0.340
## [892] 0.660 0.450 0.660 0.630 0.590 0.310 0.590 0.310 1.020 0.310 0.635
## [903] 0.635 0.590 0.590 0.580 0.540 0.560 0.520 0.305 0.380 0.280 0.460
## [914] 0.395 0.305 0.315 0.715 0.410 0.360 0.620 0.410 0.360 0.620 0.410
## [925] 0.470 0.220 0.240 0.670 0.470 0.330 0.610 0.610 0.400 0.610 0.610
## [936] 0.300 0.300 0.630 0.380 0.460 0.330 0.270 0.430 0.500 0.300 0.440
## [947] 0.440 0.280 0.120 0.120 0.120 0.280 0.310 0.340 0.430 0.210 0.360
## [958] 0.370 0.570 0.590 0.470 0.560 0.570 0.270 0.470 0.340 0.380 0.660
## [969] 0.400 0.560 0.260 0.260 0.380 0.340 0.330 0.410 0.410 0.590 0.400
## [980] 0.450 0.500 0.860 0.520 0.500 0.450 0.580 0.340 0.360 0.390 0.295
## [991] 0.390 0.340 0.400 0.340 0.350 0.600 0.660 0.660 0.840 0.690 0.430
## [1002] 0.350 0.290 0.360 0.430 0.360 0.290 0.300 0.350 0.500 0.280 0.320
## [1013] 1.005 0.710 0.580 0.390 0.380 0.180 0.180 0.500 0.360 0.360 0.510
## [1024] 0.320 0.580 0.830 0.310 0.795 0.340 0.580 0.590 0.550 0.820 0.570
## [1035] 0.745 0.370 0.310 0.910 0.410 0.500 0.965 0.490 0.500 0.390 0.390
## [1046] 0.440 0.780 0.430 0.490 0.500 0.430 0.460 0.605 0.330 0.640 0.640
## [1057] 0.480 0.420 0.530 0.480 0.230 0.400 0.380 0.290 0.740 0.610 0.520
## [1068] 0.310 0.310 0.620 0.330 0.770 0.350 0.620 0.770 0.250 0.320 0.370
## [1079] 0.370 0.300 0.270 0.300 0.380 0.420 0.380 0.480 0.340 0.190 0.410
## [1090] 0.410 0.260 0.340 0.540 0.310 0.725 0.400 0.725 0.520 0.310 0.520
## [1101] 0.340 0.490 0.480 0.490 0.480 0.570 0.230 0.300 0.780 0.470 0.530
## [1112] 0.420 0.330 0.240 0.400 0.690 0.690 0.690 0.390 0.660 0.540 0.500
## [1123] 0.470 0.400 0.580 0.240 0.290 0.760 0.430 0.430 0.600 0.190 0.360
## [1134] 0.480 0.280 0.250 0.520 0.520 0.410 0.510 0.400 0.380 0.450 0.220
## [1145] 0.320 0.200 0.500 0.410 0.390 0.350 0.330 0.580 0.600 0.420 0.580
## [1156] 0.600 0.180 0.510 0.410 0.410 0.360 0.450 0.320 0.785 0.785 0.440
## [1167] 0.540 0.330 0.340 0.500 0.360 0.590 0.420 0.360 0.360 0.610 0.880
## [1178] 0.660 0.915 0.350 0.350 0.390 0.400 0.660 0.640 0.430 0.800 0.430
## [1189] 0.640 0.955 0.400 0.885 0.250 0.885 0.745 0.430 0.580 0.570 0.260
## [1200] 0.580 0.570 0.340 0.420 0.740 0.360 0.360 0.360 0.720 0.360 0.390
## [1211] 0.650 0.440 0.650 0.380 0.330 0.270 0.570 0.340 0.400 0.390 0.320
## [1222] 0.320 0.530 0.360 0.390 0.460 0.580 0.580 0.420 0.430 0.180 0.815
## [1233] 0.430 0.230 0.750 0.330 0.550 0.750 0.730 0.670 0.610 0.370 0.400
## [1244] 0.560 0.290 0.550 0.740 0.550 0.410 0.600 0.600 0.580 0.720 0.660
## [1255] 0.700 0.640 0.590 0.580 0.640 0.640 0.635 1.020 0.450 0.780 0.370
## [1266] 0.570 0.570 0.430 0.410 0.490 0.380 0.440 0.460 0.580 0.580 0.715
## [1277] 0.400 0.690 0.715 0.300 0.460 0.460 0.765 0.630 0.420 0.370 0.160
## [1288] 0.600 0.600 0.600 0.740 0.635 0.395 0.755 0.635 0.630 0.630 0.530
## [1299] 0.600 1.580 0.645 0.860 0.370 0.280 0.790 0.610 0.690 0.680 0.690
## [1310] 0.620 0.610 0.510 1.180 0.360 0.360 0.630 0.740 0.440 0.630 0.760
## [1321] 0.660 0.740 0.340 0.360 0.460 0.460 0.460 0.460 0.520 0.600 0.600
## [1332] 0.870 0.390 0.775 0.835 0.580 0.500 0.500 0.500 0.510 0.510 0.510
## [1343] 0.540 0.510 0.420 0.440 0.590 0.655 0.655 0.570 0.600 0.620 0.645
## [1354] 0.645 0.580 0.320 0.340 0.430 0.640 0.475 0.540 0.850 0.475 0.830
## [1365] 0.605 0.500 0.740 0.540 0.770 0.610 0.780 0.580 0.780 0.750 0.815
## [1376] 0.560 0.885 0.490 0.450 0.570 0.570 0.830 0.600 0.600 0.755 0.810
## [1387] 0.640 0.640 0.640 0.480 0.490 0.640 0.620 0.520 0.570 0.685 0.675
## [1398] 0.590 0.600 0.670 0.690 0.690 0.300 0.330 0.500 0.280 0.240 0.510
## [1409] 0.290 0.510 0.960 0.470 0.240 0.570 0.320 0.580 0.320 0.340 0.530
## [1420] 0.640 0.530 0.400 0.540 0.530 0.260 0.260 0.230 0.410 0.640 0.180
## [1431] 0.410 0.430 0.440 0.400 0.540 0.540 0.380 0.915 0.590 0.670 0.370
## [1442] 0.785 0.630 0.580 0.670 0.785 0.630 0.670 0.580 0.380 0.370 0.320
## [1453] 0.580 0.490 0.450 0.900 0.540 0.490 0.290 0.200 0.420 0.785 0.640
## [1464] 0.630 0.590 0.590 0.480 1.040 0.480 0.980 0.690 0.700 0.350 0.600
## [1475] 0.500 0.470 0.500 0.470 0.875 0.280 0.620 0.280 0.580 0.330 0.910
## [1486] 0.655 0.680 0.640 0.540 0.570 0.220 0.540 0.650 0.540 0.310 0.430
## [1497] 0.540 0.740 0.895 0.740 0.725 0.820 0.585 0.440 0.380 0.760 0.810
## [1508] 0.380 0.270 0.180 0.360 0.690 0.790 0.560 0.840 0.840 0.320 0.530
## [1519] 0.470 0.700 0.530 0.480 0.320 0.480 0.420 0.480 0.470 0.530 0.290
## [1530] 0.690 0.440 0.705 0.530 0.390 0.560 0.550 0.530 0.580 0.640 0.390
## [1541] 0.520 0.250 0.855 0.440 0.370 0.630 0.570 0.600 0.400 0.360 0.680
## [1552] 0.670 0.680 0.735 0.855 0.560 0.880 0.855 0.630 0.600 0.600 0.600
## [1563] 0.695 0.695 0.695 0.670 0.160 0.695 0.560 0.510 0.360 0.380 0.690
## [1574] 0.580 0.310 0.520 0.300 0.700 0.670 0.560 0.350 0.560 0.715 0.460
## [1585] 0.320 0.390 0.310 0.610 0.660 0.725 0.550 0.740 0.510 0.620 0.600
## [1596] 0.550 0.510 0.645 0.310## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 4 rows containing non-finite values (stat_bin).
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## [1] 1.90 2.60 2.30 1.90 1.90 1.80 1.60 1.20 2.00 6.10 1.80
## [12] 6.10 1.60 1.60 3.80 3.90 1.80 1.70 4.40 1.80 1.80 2.30
## [23] 1.60 2.30 2.40 1.40 1.80 1.60 1.90 2.00 2.40 2.50 2.30
## [34] 10.70 1.80 5.50 2.40 2.10 1.50 5.90 5.90 2.80 2.60 2.20
## [45] 1.80 2.10 2.20 1.60 1.60 1.40 1.70 2.20 2.10 3.00 2.80
## [56] 3.80 3.40 5.10 2.30 2.40 2.20 1.80 1.90 2.00 4.65 4.65
## [67] 1.50 1.60 2.00 1.90 1.90 2.10 1.90 2.10 2.50 2.20 2.20
## [78] 2.40 2.00 1.50 1.60 1.90 2.00 1.80 1.80 2.20 1.90 1.90
## [89] 2.10 1.80 1.90 1.90 2.00 1.90 1.40 2.30 3.00 2.00 2.50
## [100] 1.90 2.10 1.90 1.90 2.10 2.20 2.10 1.70 1.70 2.50 2.00
## [111] 1.80 2.20 2.20 2.30 1.80 2.20 1.90 2.00 2.20 1.80 1.70
## [122] 2.20 2.50 2.60 1.60 1.90 1.70 1.80 1.80 1.80 2.00 2.30
## [133] 2.30 1.50 2.20 1.90 1.80 2.00 2.10 2.00 1.90 1.80 1.80
## [144] 1.70 1.80 1.80 1.80 1.60 2.30 2.80 2.10 3.40 1.80 1.80
## [155] 5.50 5.50 5.50 5.50 2.20 1.90 2.00 1.30 1.70 7.30 7.20
## [166] 1.70 2.10 1.60 2.10 1.80 1.80 2.00 2.00 1.90 2.00 1.50
## [177] 2.00 2.30 2.50 2.40 2.40 2.00 2.50 1.80 1.90 2.00 2.00
## [188] 2.60 2.00 1.90 2.90 1.90 3.80 2.20 2.20 2.00 2.40 2.00
## [199] 1.20 2.10 1.40 2.10 1.50 1.60 1.60 2.60 2.60 1.80 2.70
## [210] 2.10 2.00 2.80 2.10 2.20 2.40 5.60 2.00 2.20 1.90 2.40
## [221] 2.00 2.00 1.50 2.00 2.00 2.60 2.00 2.60 2.60 2.60 1.60
## [232] 1.80 2.80 2.60 2.30 1.90 1.90 1.90 1.90 2.30 1.70 2.10
## [243] 1.80 2.20 2.20 2.00 1.90 2.30 1.70 2.00 1.60 1.80 3.10
## [254] 1.90 1.80 3.20 2.20 2.10 1.80 2.60 1.70 2.00 1.70 1.80
## [265] 2.40 1.80 3.30 3.60 3.00 4.00 4.00 4.00 4.00 2.40 7.00
## [276] 4.00 3.00 4.00 6.40 5.60 3.60 3.50 3.00 5.60 3.40 3.40
## [287] 2.00 3.00 2.50 3.30 2.50 2.00 2.70 2.40 3.20 2.50 2.60
## [298] 2.00 2.30 2.10 2.60 1.50 2.60 1.60 2.10 2.50 2.20 2.40
## [309] 2.40 1.70 2.50 2.00 2.80 3.00 2.60 2.50 3.40 2.90 3.20
## [320] 2.90 3.20 3.40 2.30 2.80 11.00 11.00 3.65 4.50 2.60 2.00
## [331] 2.90 2.90 3.20 2.10 2.50 3.40 1.90 2.80 3.00 2.30 2.40
## [342] 2.70 1.80 1.80 2.60 1.90 2.70 3.00 2.80 2.60 2.70 2.60
## [353] 2.40 4.80 1.40 2.40 3.00 2.95 3.10 2.60 2.00 2.60 2.50
## [364] 2.00 5.80 3.40 5.80 2.60 2.80 2.40 2.30 1.60 1.80 2.20
## [375] 3.80 4.40 3.00 2.40 6.20 2.50 2.00 2.90 2.00 2.00 2.10
## [386] 2.40 2.00 1.90 1.90 2.50 1.40 2.90 2.00 2.00 2.30 4.20
## [397] 7.90 2.60 2.60 2.30 7.90 1.70 2.60 2.70 2.70 1.40 2.50
## [408] 3.00 3.70 4.50 2.50 2.40 1.90 6.70 2.70 6.60 2.20 1.90
## [419] 2.00 1.80 2.40 2.30 2.00 2.10 2.00 2.30 2.10 1.90 1.30
## [430] 2.40 2.10 2.20 2.30 2.30 3.20 2.30 2.00 3.20 3.20 1.50
## [441] 2.20 2.15 3.70 2.70 1.70 2.10 2.60 2.10 2.00 2.80 2.80
## [452] 1.80 1.70 2.80 1.60 5.20 2.30 2.70 2.80 2.20 2.30 2.60
## [463] 2.55 2.20 2.10 2.90 2.00 2.60 2.10 1.20 2.60 2.40 2.60
## [474] 2.10 1.70 2.20 2.00 1.80 2.20 2.70 15.50 2.80 2.20 2.20
## [485] 4.10 1.90 1.90 1.80 2.80 2.60 2.80 2.50 2.60 3.00 8.30
## [496] 2.60 1.90 2.50 2.60 3.00 1.90 6.55 6.55 1.90 1.80 2.90
## [507] 1.80 2.30 2.20 2.80 4.60 2.20 2.10 2.40 2.40 6.10 4.30
## [518] 2.10 2.80 2.50 2.70 2.00 2.30 2.50 2.40 2.80 2.50 2.50
## [529] 2.60 2.40 2.10 2.70 2.70 2.10 2.70 2.10 2.40 2.10 5.80
## [540] 5.15 3.30 6.30 2.10 2.50 1.80 2.60 2.00 2.50 2.60 1.90
## [551] 2.10 2.80 2.70 1.60 4.20 4.20 4.60 4.20 4.60 4.30 2.80
## [562] 2.40 2.90 2.70 4.30 2.80 2.50 2.50 2.60 2.20 3.30 2.20
## [573] 2.40 2.10 3.20 3.10 2.30 2.80 2.90 2.20 2.20 2.20 2.20
## [584] 1.90 3.40 2.40 2.70 1.90 2.00 2.60 2.60 1.70 2.60 3.50
## [595] 2.60 7.90 2.00 1.90 2.10 2.30 2.10 2.20 2.60 2.20 2.90
## [606] 2.60 4.60 3.30 5.10 3.20 2.50 2.70 2.40 1.50 2.20 2.30
## [617] 2.30 2.20 2.70 2.30 3.40 3.40 1.90 2.90 5.60 5.60 2.20
## [628] 2.20 2.50 2.30 2.50 2.70 3.00 3.40 1.90 1.40 2.40 2.30
## [639] 2.20 1.90 2.30 2.30 2.30 2.30 2.30 6.00 3.60 2.20 2.80
## [650] 8.60 2.20 2.50 7.50 2.80 2.40 2.90 2.20 1.40 1.40 4.40
## [661] 1.40 1.60 1.60 1.80 2.00 2.00 1.80 2.00 2.30 2.00 2.50
## [672] 1.70 2.00 1.70 2.20 2.20 2.20 2.30 2.60 3.30 1.90 2.20
## [683] 2.25 2.60 2.30 2.60 1.80 3.10 1.60 1.80 4.25 2.60 2.00
## [694] 2.80 2.70 1.30 2.10 2.10 3.20 2.10 2.90 2.10 2.10 2.60
## [705] 1.60 6.00 2.00 3.00 2.50 1.60 2.80 3.00 3.20 2.30 2.60
## [716] 2.70 2.30 2.60 2.00 3.90 2.00 2.85 2.70 2.20 3.10 3.00
## [727] 2.80 1.80 1.80 3.20 2.30 3.45 2.10 2.70 2.00 2.10 2.10
## [738] 2.50 2.80 2.40 4.20 2.60 1.90 2.80 2.70 2.10 2.50 2.60
## [749] 2.10 2.10 2.90 2.90 2.50 2.90 1.70 1.90 2.00 2.20 2.20
## [760] 2.50 2.80 2.00 1.70 2.00 2.80 3.00 2.90 2.70 2.30 1.90
## [771] 2.30 2.40 2.30 1.80 1.80 3.00 2.40 2.40 3.40 2.60 2.00
## [782] 2.40 2.40 2.40 2.50 2.30 2.30 2.20 2.20 2.90 2.60 2.90
## [793] 2.50 2.60 2.30 2.60 2.50 1.60 3.60 3.60 4.00 3.30 1.70
## [804] 2.50 2.70 2.40 2.00 2.40 1.90 2.80 2.60 2.80 2.50 2.10
## [815] 2.80 2.50 3.20 1.60 2.35 3.20 1.90 2.10 2.00 2.00 2.80
## [826] 2.80 2.30 2.80 2.30 2.10 2.50 2.10 1.50 1.60 1.60 1.50
## [837] 2.40 2.40 1.60 2.20 2.65 3.00 2.60 2.00 1.70 1.80 1.80
## [848] 1.80 1.80 1.60 1.90 1.90 2.50 1.50 1.50 2.50 1.50 2.50
## [859] 1.70 1.80 2.70 2.00 2.70 2.50 2.70 2.60 2.30 2.00 1.80
## [870] 2.00 2.10 1.50 2.00 1.60 2.10 2.80 2.20 2.10 4.00 2.50
## [881] 1.60 2.10 3.10 2.50 4.00 2.50 2.40 2.60 2.50 6.60 2.00
## [892] 2.30 1.90 2.30 2.20 2.30 2.40 2.30 2.40 3.40 2.60 2.40
## [903] 2.40 6.00 6.00 3.00 2.60 2.20 2.40 1.20 3.80 9.00 2.90
## [914] 4.60 1.20 2.20 1.50 8.80 2.20 1.80 2.30 2.20 1.80 8.80
## [925] 2.30 1.90 2.30 2.20 2.30 3.30 1.90 2.00 1.90 2.00 1.90
## [936] 2.30 2.30 1.40 2.80 1.60 2.20 5.00 2.60 2.30 3.80 2.00
## [947] 4.10 2.10 1.80 1.80 1.80 2.10 2.20 2.10 2.70 1.90 2.10
## [958] 2.00 2.30 2.00 1.90 1.60 2.10 2.00 1.90 2.40 2.40 2.10
## [969] 2.40 2.90 1.90 1.90 2.40 1.70 5.90 2.10 2.10 2.60 3.60
## [980] 1.40 1.90 1.90 2.10 1.90 1.40 2.00 1.40 1.60 1.70 1.50
## [991] 1.70 2.00 2.00 2.00 2.50 2.00 2.20 2.20 1.40 1.65 2.20
## [1002] 1.50 2.05 1.80 1.60 1.80 2.05 2.00 3.60 2.80 1.70 2.00
## [1013] 2.10 1.60 2.00 2.20 2.20 0.90 0.90 1.80 2.40 2.40 2.10
## [1024] 2.30 1.80 2.80 1.90 2.20 2.50 1.80 2.10 1.80 4.10 2.60
## [1035] 2.50 2.40 2.50 1.80 6.20 2.20 2.20 1.70 2.20 8.90 3.30
## [1046] 1.40 1.70 1.80 1.70 1.80 1.80 1.40 2.40 2.30 2.00 2.00
## [1057] 4.00 3.90 2.40 4.00 1.80 1.80 1.90 2.40 2.00 2.40 2.40
## [1068] 2.20 2.20 2.80 1.50 8.10 1.80 2.70 8.10 2.00 2.00 6.40
## [1079] 6.40 8.30 1.40 8.30 1.80 2.40 1.80 1.80 4.70 1.60 1.50
## [1090] 1.50 1.90 2.00 2.00 2.20 5.50 2.50 5.50 1.50 2.10 1.50
## [1101] 2.10 2.10 1.70 2.10 2.20 2.10 1.90 2.00 3.30 2.10 1.40
## [1112] 2.00 1.50 1.60 4.30 2.50 2.50 2.50 2.10 2.50 2.50 1.80
## [1123] 1.40 1.90 2.20 1.70 1.70 2.90 2.70 3.30 1.90 1.70 1.80
## [1134] 5.50 1.70 1.70 2.00 2.00 3.70 2.00 1.70 2.50 2.40 1.80
## [1145] 2.30 2.50 1.80 6.20 2.00 2.00 2.80 2.50 2.20 2.10 2.20
## [1156] 2.20 1.75 2.10 2.80 2.20 2.30 1.40 2.30 1.70 1.70 1.90
## [1167] 2.00 2.50 2.80 2.30 1.60 2.20 2.10 1.70 1.70 2.20 5.60
## [1178] 2.40 2.10 2.40 2.40 1.65 2.50 1.60 2.10 2.00 7.80 2.00
## [1189] 2.10 1.80 4.60 2.30 2.50 2.30 1.80 1.80 2.30 1.50 2.00
## [1200] 2.30 1.50 1.90 1.80 5.80 2.10 2.10 2.10 1.70 2.10 2.00
## [1211] 2.10 2.10 2.10 1.90 1.90 2.10 2.00 1.90 1.90 1.30 1.80
## [1222] 1.80 2.20 2.20 2.50 2.60 4.10 2.00 1.80 2.10 2.70 2.60
## [1233] 2.10 2.20 2.20 12.90 1.70 2.20 2.50 4.30 1.70 2.50 2.00
## [1244] 2.40 13.40 1.80 1.70 1.80 2.20 2.30 2.30 2.20 1.80 1.40
## [1255] 1.90 2.40 1.80 4.80 2.70 2.70 1.80 2.00 2.50 2.20 1.80
## [1266] 2.30 2.30 2.30 2.00 1.80 1.60 1.60 1.90 2.00 2.10 2.30
## [1277] 6.30 1.90 2.30 1.70 1.90 1.90 2.00 2.70 2.30 1.80 2.50
## [1288] 2.60 4.50 4.50 1.90 2.10 2.40 1.90 2.10 4.30 4.30 2.10
## [1299] 1.40 2.10 2.15 2.00 2.10 1.80 2.30 1.90 2.50 3.90 2.50
## [1310] 1.40 1.90 3.00 1.90 2.30 2.40 2.00 1.20 2.20 2.00 1.70
## [1321] 2.60 1.20 1.80 1.80 1.70 1.70 1.70 1.70 1.80 2.10 2.10
## [1332] 3.80 1.70 2.20 2.00 2.40 1.40 1.40 1.40 1.70 1.70 1.70
## [1343] 1.70 1.70 2.60 2.30 2.10 1.80 1.80 2.80 2.00 2.30 1.90
## [1354] 1.90 2.30 1.80 1.80 2.50 5.40 1.40 2.30 2.50 1.40 2.00
## [1365] 1.90 2.20 1.70 2.20 2.10 1.60 1.70 3.10 1.70 3.80 1.20
## [1376] 2.00 1.40 2.30 2.00 2.60 2.60 1.80 2.10 2.10 1.80 3.40
## [1387] 1.80 1.80 6.10 2.20 2.30 2.40 1.30 2.00 3.90 1.60 1.60
## [1398] 2.00 2.20 2.20 2.10 2.10 2.00 1.70 2.60 2.00 5.10 2.10
## [1409] 2.20 2.10 1.80 2.40 5.10 2.00 2.20 1.60 2.20 2.50 1.60
## [1420] 2.20 1.60 1.60 2.10 3.90 1.40 1.40 1.80 2.50 1.90 2.20
## [1431] 1.80 2.10 1.60 1.80 15.40 15.40 1.60 4.80 1.70 2.20 2.00
## [1442] 5.20 1.90 1.75 2.20 5.20 1.90 1.90 1.90 2.00 2.00 2.70
## [1453] 2.00 1.90 2.20 1.60 1.80 1.90 1.70 1.70 2.30 2.10 2.30
## [1464] 2.40 1.70 1.70 2.10 2.30 2.10 2.10 1.40 3.75 2.60 1.80
## [1475] 13.80 2.20 13.80 2.20 5.70 3.00 1.50 3.00 2.10 1.50 2.00
## [1486] 2.10 2.10 1.90 1.70 2.10 1.80 1.70 1.60 1.90 1.40 1.90
## [1497] 1.90 2.30 2.30 2.30 1.50 4.30 2.40 2.50 2.30 1.80 2.00
## [1508] 2.30 2.10 1.80 2.20 2.10 2.20 1.80 4.10 4.10 2.30 2.00
## [1519] 2.20 2.60 2.00 1.90 2.30 2.00 2.00 2.10 2.20 1.70 2.20
## [1530] 2.10 2.20 2.80 2.00 1.90 2.40 2.20 1.90 1.90 2.50 1.80
## [1541] 4.40 2.20 1.90 2.20 2.30 1.80 2.00 1.60 2.00 1.80 2.30
## [1552] 2.30 3.70 2.20 2.40 1.70 2.20 2.40 6.70 2.00 2.00 2.00
## [1563] 2.00 2.00 2.00 1.90 2.10 2.00 1.60 1.90 2.20 2.20 2.20
## [1574] 2.40 13.90 2.20 1.60 5.10 1.80 1.70 2.40 1.70 2.60 2.10
## [1585] 2.40 2.60 2.40 1.80 2.50 7.80 1.80 1.70 2.30 1.90 2.00
## [1596] 2.20 2.30 2.00 3.60## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.01200 0.07000 0.07900 0.08747 0.09000 0.61100## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 2 rows containing non-finite values (stat_bin).
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1.00 7.00 14.00 15.87 21.00 72.00## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 4 rows containing non-finite values (stat_bin).
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 6.00 22.00 38.00 46.47 62.00 289.00## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 2 rows containing non-finite values (stat_bin).
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.9901 0.9956 0.9968 0.9967 0.9978 1.0037## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
We divide the data into 2 groups: high quality group contains observations whose quality is 7 or 8, and low quality group has observations whose quality is 3 or 4. After examining the difference in each feature between the two groups, we see that volatile acidity, density, and citric acid may have some correation with quality. Let’s visualize the data to see the difference.
#subset the wine with high quality which is 7 and 8
quality_high <- subset(wine, quality == 8 | quality == 7)
#subset the wine with low quality which is 3 and 4
quality_low <- subset(wine, quality == 3 | quality == 4)
#plot volatile vs quality
volatileVsHighquality<-qplot(x=quality_high$volatile.acidity, data=quality_high,
xlab="Volatile acidity (g/dm^3), quality_high",
binwidth=0.1)
volatileVsLowquality <- qplot(x=quality_low$volatile.acidity, data=quality_low,
xlab="Volatile acidity (g/dm^3), quality_low",
binwidth=0.1)
grid.arrange(volatileVsHighquality,volatileVsLowquality)
#红酒质量越好，挥发性越低it seems that density has no correlation with quality
densityVsHighquality<-qplot(x=quality_high$density, data=quality_high,
xlab="Density (g/dm^3), quality_high")
densityVslowquality<-qplot(x=quality_low$density, data=quality_low,
xlab="Density (g/dm^3), quality_low")
grid.arrange(densityVsHighquality,densityVslowquality)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
citric.acid 越高，质量越好
citric.acidVsHighquality<-qplot(x=quality_high$citric.acid, data=quality_high,
xlab="citric.acid (g/dm^3), quality_high")
citric.acidVslowquality<-qplot(x=quality_low$citric.acid, data=quality_low,
xlab="citric.acid (g/dm^3), quality_low")
grid.arrange(citric.acidVsHighquality,citric.acidVslowquality)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
alcoholVsHighquality<-qplot(x=quality_high$alcohol, data=quality_high,
xlab="alcohol (g/dm^3), quality_high")
alcoholVslowquality<-qplot(x=quality_low$alcohol, data=quality_low,
xlab="alcohol (g/dm^3), quality_low")
grid.arrange(alcoholVsHighquality,alcoholVslowquality)## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Univariate Analysis
Tip: Now that you’ve completed your univariate explorations, it’s time to reflect on and summarize what you’ve found. Use the questions below to help you gather your observations and add your own if you have other thoughts!
What is the structure of your dataset?
There are 1,599 red wines in the dataset with 11 features on the chemical properties of the wine. ( fixed.acidity, volatile.acidity, citric.acid, residual.sugar, chlorides, free.sulfur.dioxide, total.sulfur.dioxide, density, pH, sulphates, alcohol, and quality).
What is/are the main feature(s) of interest in your dataset?
i would like to know which factor determine or has corelation with the quality of the wine.
What other features in the dataset do you think will help support yourinvestigation into your feature(s) of interest?
Volatile acidity, citric acid, and alcohol seems contribute to the quality of a wine.However, density seems has no relationship with the qualoty of the wine.
I think volatile acidityl,citric acid, alcohol probably contribute most to the quality.
Did you create any new variables from existing variables in the dataset?
Yes, I created a new variable quality.level. It divided into the quality as “low”, “average”, and “high”.
Of the features you investigated, were there any unusual distributions?
Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this? This dataset is preety clean, I think i dont have to do the cleaning job.
Bivariate Plots Section
Tip: Based on what you saw in the univariate plots, what relationships between variables might be interesting to look at in this section? Don’t limit yourself to relationships between a main output feature and one of the supporting variables. Try to look at relationships between supporting variables as well.
The graph shows a very clear trend; the lower volatile acidity is, the higher the quality becomes.
ggplot(aes(x=quality.level, y=citric.acid), data=wine) +
geom_point(alpha=0.5,
position=position_jitter(h=0),
color='orange')+
geom_boxplot(alpha=0.1)+
xlab("Quality level") +
ylab("citric.acid")
The graph shows there is no positive relationship between quality level and citric acid.
ggplot(aes(x=quality.level, y=fixed.acidity), data=wine) +
geom_point(alpha=0.5,
position=position_jitter(h=0),
color='orange')+
geom_boxplot(alpha=0.1)+
xlab("Quality level") +
ylab("fixed.acidity")
The graph shows there is no positive relationship between quality level and citric acid.
ggplot(aes(x=quality.level, y=alcohol), data=wine) +
geom_point(alpha=0.5,
position=position_jitter(h=0),
color='orange')+
xlab("Quality level") +
ylab("alcohol")
the correlation coefficient of 0.476, the graph shows a positive relationship between alcohol and quality level.
#the relationship between volatile vs alcohol
ggplot(aes(x=alcohol, y=volatile.acidity), data=wine) +
geom_point(
position=position_jitter(h=0),
color='orange')+
geom_smooth()+
xlab("volatile") +
ylab("alcohol")## `geom_smooth()` using method = 'gam'
A weak negative correlation of -0.2 exists between percent alcohol content and volatile acidity.
#the relationship between sugur vs alcohol
ggplot(aes(x=residual.sugar, y=alcohol), data=wine) +
geom_point(
position=position_jitter(h=0),
color='green')+
xlab("sugar") +
ylab("alcohol")
The correlation coefficient is 0.04, which indicates that there is almost no relationship between residual sugar and percent alcohol content. However,the most wine are contrented on the low sugar area.
#the relationship between citric vs volatile 柠檬酸与挥发性的关系
ggplot(aes(x=citric.acid, y=volatile.acidity), data=wine) +
geom_point(
position=position_jitter(h=0),
color='darkgreen')+
geom_smooth()+
xlab("citric.acid") +
ylab("volatile.acidity")## `geom_smooth()` using method = 'gam'
There is a negative correlation between citric acid and volatile acidity.
Bivariate Analysis
Tip: As before, summarize what you found in your bivariate explorations here. Use the questions below to guide your discussion.
Talk about some of the relationships you observed in this part of the
investigation. How did the feature(s) of interest vary with other features in
the dataset?
I found a negative relationships between quality level and volatile acidity, and positive correlation between quality level and alcohol.
Did you observe any interesting relationships between the other features
(not the main feature(s) of interest)?
The correlation coefficient between sugar and alcohol is 0.04, which indicates that there is almost no relationship between residual sugar and percent alcohol content. However,the most wine are contrented on the low sugar area.
What was the strongest relationship you found?
a negative relationships between quality level and volatile acidity, and positive correlation between quality level and alcohol.
Multivariate Plots Section
Tip: Now it’s time to put everything together. Based on what you found in the bivariate plots section, create a few multivariate plots to investigate more complex interactions between variables. Make sure that the plots that you create here are justified by the plots you explored in the previous section. If you plan on creating any mathematical models, this is the section where you will do that.
ggplot(aes(x = density, y=volatile.acidity,color = quality.level),data=wine) +
geom_point(alpha=0.5)+
xlab("Density (g/cm^3)") +
ylab("Volatile acidity (g/cm^3)") +
labs(fill="Quality level")
The densities of high quality wines are concentrated between 0.994 and 0.998, and the lower part of volatile acidity.
ggplot(aes(x =volatile.acidity, y= alcohol,
color = quality.level,
size=citric.acid),data=wine) +
geom_point(alpha=0.5)+
xlab("Volatile acidity") +
ylab("alcohol") +
labs(color="Quality level")+
labs(size="citric.acid")
The alcohol ranging from 10 to 13,the volatile acidity from 0.2 to 0.5 seems to be high quality wine.
Multivariate Analysis
Talk about some of the relationships you observed in this part of the
investigation. Were there features that strengthened each other in terms of
looking at your feature(s) of interest?
The densities of high quality wines are concentrated between 0.994 and 0.998, and the lower part of volatile acidity.
Were there any interesting or surprising interactions between features?
The alcohol ranging from 10 to 13,the volatile acidity from 0.2 to 0.5 seems to be high quality wine.
OPTIONAL: Did you create any models with your dataset? Discuss the
strengths and limitations of your model.
Final Plots and Summary
Tip: You’ve done a lot of exploration and have built up an understanding of the structure of and relationships between the variables in your dataset. Here, you will select three plots from all of your previous exploration to present here as a summary of some of your most interesting findings. Make sure that you have refined your selected plots for good titling, axis labels (with units), and good aesthetic choices (e.g. color, transparency). After each plot, make sure you justify why you chose each plot by describing what it shows.
Plot One
Description One
This plot revels that the marjority part of wines are rated 5 and 6. There exists no wine that is rated 1, 2, 9 or 10.In other word,there is no extramely bad quality wine and no extramely good wine.
Plot Two
Description Two
The graph shows a very clear trend; the lower volatile acidity is, the higher the quality becomes.
Plot Three
Description Three
The alcohol ranging from 10 to 13,the volatile acidity from 0.2 to 0.5 seems to be high quality wine.
Reflection
I still need to improve my statistics knowledge.I dont really understand how to create a predictive model. this is the most difficultie part for me.